Deposhor B Leave money in the bank Wit\'hdraw money A: $0 Leave A: $5,250 money

Question

Deposhor B Leave money in the bank Wit'hdraw money A: $0 Leave A: $5,250 money In the benk B: $5,250 B: $500 withdrow A:$500 money A: $250 B: $O B: $250 Figure 14.12 . Consider the game table for a local bank depicted in Figure 14.12. Assume there are only two customers and that a bank panic ensues. Which of the following statements is true? A) A Nash equilibrium occurs if both depositors leave their money in the bank. B) A Nash equilibrium occurs if both depositors go to the bank and withdraw as much as possible. C) There are two Nash equilibria) D) Neither player has a dominant strategy

Explanation / Answer

Consider the given problem, here there are 2 player “A”, “B” and there are 2 NE, these are (Leave money in the bank, Leave money in the bank)=(5,250, 5,250) and (Withdrew money, Withdrew money)=(250, 250).

We can see if “A” choose “Withdrew money”, then the optimum choice for “B” is “Withdrew money”, since 250 > 0. Similarly, if “B” choose “Withdrew money”, then the optimum choice for “A” is “Withdrew money”, since 250 > 0, => (Withdrew money, Withdrew money) be a NE.

Similarly, if “A” choose “Leave money in the bank”, then the optimum choice for “B” is “Leave money in the bank”, since 5,250 > 500. Similarly, if “B” choose “Leave money in the bank then the optimum choice for “A” is “Leave money in the bank”, since 5,250 > 500, => (Leave money in the bank, Leave money in the bank) be another NE.

So, there are 2 NE, these are (Leave money in the bank, Leave money in the bank) = (5,250, 5,250) and (Withdrew money, Withdrew money) = (250, 250).

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